Numbers Into Sums | Partition Theory

How many ways can you write n as sums of other positive integers? Well, our beloved Ramanujan used a lot of time on this mystery. He discovered a famous function to calculate partitions of n. Although there is still no precise function to this day... There are only algorithms for it.

Any questions?
#numbertheory #highschool #mathematics #college #combinatorics #manim

[dnuma]

theres actually an infinite amount of ways since it was never specified positive integers

[kingsmanbg]

Srinivasa Ramanujam is a legen in math!

[KingMe-qzhr]

If n = n + 0 counts, then there are Infinite possibilities. For example 2=1+1, 2=1+1+0, 2=1+1+0+0 etc

[thenixaless]

Very interesting!! thank you for the info I will wholeheartedly go read more about it ^^

[bagelnine]

Please note that of all the math people I have watched, you are among the most interesting. I know some of these math lessons are just needless complications for 1 + 1 = 2, but still.

[СергійМоскаленко-уы]

in the last formula there should be this: 1/(4*n*sqrt(3)) * exp(PI*sqrt(2*n/3))
but not this: ( 1/(4*n*sqrt(3)) )^(PI*sqrt(2*n/3))

But anyway thanks for the video, it was informative👍

[hrk]

The formula has a mistake, it is suposed to be: p(n) ~ exp(π√(2n/3))/(4n√3)

[lucasjuhlsiems]

I love the starwars theme in the background

[nomekop]

I came expecting a math shitpost and found actual math. This is really cool. I wonder if it's on the OEIS?

[antoine]

i'm pretty sure it's missing an exponential function somewhere ..

[arrow_zamtion]

Who invented this formula ? Ramanujan ❤

[aabhaS.sharma]

First of all, there are infinite ways to write 2 as the sum of two integers ex- (-3+5), (-2+4), (1+1), etc you must've written express 2 as the sum of two natural nos
saw the comment of @Dnuma and found that I am 2 days late

[krotronmastize]

Well, I don't understand how **Integers are just whole numbers!!**